Abstract

We propose and demonstrate a new, to the best of our knowledge, kind of partially coherent vector beam called the partially coherent radially polarized circular Airy beam (PCRPCAB). The PCRPCAB inherits the autofocusing ability of the radially polarized circular Airy beam (RPCAB) and can create an optical potential well at the center of the beam, whose depth can be adjusted by changing the coherent width. We find that, as coherent width decreases, the intensity becomes higher in the dark notch caused by the polarization singularity, and the singularity of the degree of polarization (DOP) remains along propagation, with its waist controllable by the coherent width. Our results make the PCRPCAB a good candidate for optical micromanipulation, disordered optical lattices, etc.

© 2020 Optical Society of America

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References

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2020 (1)

2019 (3)

2018 (2)

M. A. Norcia, A. W. Young, and A. M. Kaufman, Phys. Rev. X 8, 041054 (2018).
[Crossref]

Y. Jiang, W. Yu, X. Zhu, and P. Jiang, Opt. Express 26, 23084 (2018).
[Crossref]

2017 (1)

2016 (3)

M. W. Hyde, S. Bose-Pillai, D. G. Voelz, and X. Xiao, Phys. Rev. Appl. 6, 064030 (2016).
[Crossref]

X. Zhang, R. P. del Aguila, T. Mazzoni, N. Poli, and G. M. Tino, Phys. Rev. A 94, 043608 (2016).
[Crossref]

L. Guo, Y. Chen, X. Liu, L. Liu, and Y. Cai, Opt. Express 24, 13714 (2016).
[Crossref]

2015 (1)

2014 (3)

2013 (2)

J. Zhang, Z. Wang, B. Cheng, Q. Wang, B. Wu, X. Shen, L. Zheng, Y. Xu, and Q. Lin, Phys. Rev. A 88, 023416 (2013).
[Crossref]

J. M. Aunon and M. Nieto-Vesperinas, Opt. Lett. 38, 2869 (2013).
[Crossref]

2012 (4)

S. Ghosh, B. P. Pal, and R. Varshney, Opt. Commun. 285, 2785 (2012).
[Crossref]

G. Wu, F. Wang, and Y. Cai, Opt. Express 20, 28301 (2012).
[Crossref]

Y. Dong, F. Feng, Y. Chen, C. Zhao, and Y. Cai, Opt. Express 20, 15908 (2012).
[Crossref]

F. Wang, Y. Cai, Y. Dong, and O. Korotkova, Appl. Phys. Lett. 100, 051108 (2012).
[Crossref]

2011 (1)

2010 (1)

2009 (1)

M. White, M. Pasienski, D. McKay, S. Q. Zhou, D. Ceperley, and B. DeMarco, Phys. Rev. Lett. 102, 055301 (2009).
[Crossref]

2007 (2)

2001 (1)

1999 (1)

X. Xu, V. G. Minogin, K. Lee, Y. Wang, and W. Jhe, Phys. Rev. A 60, 4796 (1999).
[Crossref]

Aunon, J. M.

Bose-Pillai, S.

M. W. Hyde, S. Bose-Pillai, D. G. Voelz, and X. Xiao, Phys. Rev. Appl. 6, 064030 (2016).
[Crossref]

Cada, M.

Cai, Y.

Ceperley, D.

M. White, M. Pasienski, D. McKay, S. Q. Zhou, D. Ceperley, and B. DeMarco, Phys. Rev. Lett. 102, 055301 (2009).
[Crossref]

Chen, L.

Chen, Y.

Cheng, B.

J. Zhang, Z. Wang, B. Cheng, Q. Wang, B. Wu, X. Shen, L. Zheng, Y. Xu, and Q. Lin, Phys. Rev. A 88, 023416 (2013).
[Crossref]

Christodoulides, D. N.

del Aguila, R. P.

X. Zhang, R. P. del Aguila, T. Mazzoni, N. Poli, and G. M. Tino, Phys. Rev. A 94, 043608 (2016).
[Crossref]

DeMarco, B.

M. White, M. Pasienski, D. McKay, S. Q. Zhou, D. Ceperley, and B. DeMarco, Phys. Rev. Lett. 102, 055301 (2009).
[Crossref]

Dong, Y.

Efremidis, N. K.

Emil, W.

B. Max and W. Emil, Principles of Optics, 7th expanded ed. (Publishing House of Electronics Industry, 2013).

Feng, F.

Ghosh, S.

S. Ghosh, B. P. Pal, and R. Varshney, Opt. Commun. 285, 2785 (2012).
[Crossref]

Guo, L.

Hu, H.

Huang, K.

Huang, W.

Hyde, M. W.

M. W. Hyde, S. Bose-Pillai, D. G. Voelz, and X. Xiao, Phys. Rev. Appl. 6, 064030 (2016).
[Crossref]

Jhe, W.

X. Xu, V. G. Minogin, K. Lee, Y. Wang, and W. Jhe, Phys. Rev. A 60, 4796 (1999).
[Crossref]

Jiang, P.

Jiang, Y.

Kaufman, A. M.

M. A. Norcia, A. W. Young, and A. M. Kaufman, Phys. Rev. X 8, 041054 (2018).
[Crossref]

Korotkova, O.

F. Wang, Y. Cai, Y. Dong, and O. Korotkova, Appl. Phys. Lett. 100, 051108 (2012).
[Crossref]

Lancis, J.

Lee, K.

X. Xu, V. G. Minogin, K. Lee, Y. Wang, and W. Jhe, Phys. Rev. A 60, 4796 (1999).
[Crossref]

Li, N.

Li, X.

Liang, C.

Lin, Q.

J. Zhang, Z. Wang, B. Cheng, Q. Wang, B. Wu, X. Shen, L. Zheng, Y. Xu, and Q. Lin, Phys. Rev. A 88, 023416 (2013).
[Crossref]

Liu, L.

Liu, X.

Lu, X.

Lu, X. H.

Mao, H.

Max, B.

B. Max and W. Emil, Principles of Optics, 7th expanded ed. (Publishing House of Electronics Industry, 2013).

Mazzoni, T.

X. Zhang, R. P. del Aguila, T. Mazzoni, N. Poli, and G. M. Tino, Phys. Rev. A 94, 043608 (2016).
[Crossref]

McKay, D.

M. White, M. Pasienski, D. McKay, S. Q. Zhou, D. Ceperley, and B. DeMarco, Phys. Rev. Lett. 102, 055301 (2009).
[Crossref]

Mendoza-Yero, O.

Mi, C.

Mínguez-Vega, G.

Minogin, V. G.

X. Xu, V. G. Minogin, K. Lee, Y. Wang, and W. Jhe, Phys. Rev. A 60, 4796 (1999).
[Crossref]

Nieto-Vesperinas, M.

Norcia, M. A.

M. A. Norcia, A. W. Young, and A. M. Kaufman, Phys. Rev. X 8, 041054 (2018).
[Crossref]

Pal, B. P.

S. Ghosh, B. P. Pal, and R. Varshney, Opt. Commun. 285, 2785 (2012).
[Crossref]

Pasienski, M.

M. White, M. Pasienski, D. McKay, S. Q. Zhou, D. Ceperley, and B. DeMarco, Phys. Rev. Lett. 102, 055301 (2009).
[Crossref]

Poli, N.

X. Zhang, R. P. del Aguila, T. Mazzoni, N. Poli, and G. M. Tino, Phys. Rev. A 94, 043608 (2016).
[Crossref]

Ponomarenko, S. A.

Shao, H.

Shen, X.

J. Zhang, Z. Wang, B. Cheng, Q. Wang, B. Wu, X. Shen, L. Zheng, Y. Xu, and Q. Lin, Phys. Rev. A 88, 023416 (2013).
[Crossref]

Sun, M.

Tino, G. M.

X. Zhang, R. P. del Aguila, T. Mazzoni, N. Poli, and G. M. Tino, Phys. Rev. A 94, 043608 (2016).
[Crossref]

Varshney, R.

S. Ghosh, B. P. Pal, and R. Varshney, Opt. Commun. 285, 2785 (2012).
[Crossref]

Voelz, D. G.

M. W. Hyde, S. Bose-Pillai, D. G. Voelz, and X. Xiao, Phys. Rev. Appl. 6, 064030 (2016).
[Crossref]

Wang, F.

Wang, L. G.

Wang, L. Q.

Wang, Q.

J. Zhang, Z. Wang, B. Cheng, Q. Wang, B. Wu, X. Shen, L. Zheng, Y. Xu, and Q. Lin, Phys. Rev. A 88, 023416 (2013).
[Crossref]

Wang, Y.

X. Xu, V. G. Minogin, K. Lee, Y. Wang, and W. Jhe, Phys. Rev. A 60, 4796 (1999).
[Crossref]

Wang, Z.

J. Zhang, Z. Wang, B. Cheng, Q. Wang, B. Wu, X. Shen, L. Zheng, Y. Xu, and Q. Lin, Phys. Rev. A 88, 023416 (2013).
[Crossref]

White, M.

M. White, M. Pasienski, D. McKay, S. Q. Zhou, D. Ceperley, and B. DeMarco, Phys. Rev. Lett. 102, 055301 (2009).
[Crossref]

Wolf, E.

E. Wolf, Introduction to the Theory of Coherence and Polarization of Light (Cambridge University, 2007).

Wu, B.

J. Zhang, Z. Wang, B. Cheng, Q. Wang, B. Wu, X. Shen, L. Zheng, Y. Xu, and Q. Lin, Phys. Rev. A 88, 023416 (2013).
[Crossref]

Wu, G.

Xiao, X.

M. W. Hyde, S. Bose-Pillai, D. G. Voelz, and X. Xiao, Phys. Rev. Appl. 6, 064030 (2016).
[Crossref]

Xu, X.

X. Xu, V. G. Minogin, K. Lee, Y. Wang, and W. Jhe, Phys. Rev. A 60, 4796 (1999).
[Crossref]

Xu, Y.

J. Zhang, Z. Wang, B. Cheng, Q. Wang, B. Wu, X. Shen, L. Zheng, Y. Xu, and Q. Lin, Phys. Rev. A 88, 023416 (2013).
[Crossref]

Xu, Z.

Yao, M.

Young, A. W.

M. A. Norcia, A. W. Young, and A. M. Kaufman, Phys. Rev. X 8, 041054 (2018).
[Crossref]

Yu, W.

Zhang, J.

M. Sun, J. Zhang, N. Li, K. Huang, H. Hu, X. Zhang, and X. Lu, Opt. Express 27, 27777 (2019).
[Crossref]

J. Zhang, Z. Wang, B. Cheng, Q. Wang, B. Wu, X. Shen, L. Zheng, Y. Xu, and Q. Lin, Phys. Rev. A 88, 023416 (2013).
[Crossref]

Zhang, X.

M. Sun, J. Zhang, N. Li, K. Huang, H. Hu, X. Zhang, and X. Lu, Opt. Express 27, 27777 (2019).
[Crossref]

X. Zhang, R. P. del Aguila, T. Mazzoni, N. Poli, and G. M. Tino, Phys. Rev. A 94, 043608 (2016).
[Crossref]

Zhao, C.

Zhao, C. L.

Zheng, L.

J. Zhang, Z. Wang, B. Cheng, Q. Wang, B. Wu, X. Shen, L. Zheng, Y. Xu, and Q. Lin, Phys. Rev. A 88, 023416 (2013).
[Crossref]

Zheng, W.

Zhou, S. Q.

M. White, M. Pasienski, D. McKay, S. Q. Zhou, D. Ceperley, and B. DeMarco, Phys. Rev. Lett. 102, 055301 (2009).
[Crossref]

Zhu, S. Y.

Zhu, X.

Appl. Phys. Lett. (1)

F. Wang, Y. Cai, Y. Dong, and O. Korotkova, Appl. Phys. Lett. 100, 051108 (2012).
[Crossref]

J. Opt. Soc. Am. A (1)

Opt. Commun. (1)

S. Ghosh, B. P. Pal, and R. Varshney, Opt. Commun. 285, 2785 (2012).
[Crossref]

Opt. Express (11)

Opt. Lett. (7)

Phys. Rev. A (3)

J. Zhang, Z. Wang, B. Cheng, Q. Wang, B. Wu, X. Shen, L. Zheng, Y. Xu, and Q. Lin, Phys. Rev. A 88, 023416 (2013).
[Crossref]

X. Zhang, R. P. del Aguila, T. Mazzoni, N. Poli, and G. M. Tino, Phys. Rev. A 94, 043608 (2016).
[Crossref]

X. Xu, V. G. Minogin, K. Lee, Y. Wang, and W. Jhe, Phys. Rev. A 60, 4796 (1999).
[Crossref]

Phys. Rev. Appl. (1)

M. W. Hyde, S. Bose-Pillai, D. G. Voelz, and X. Xiao, Phys. Rev. Appl. 6, 064030 (2016).
[Crossref]

Phys. Rev. Lett. (1)

M. White, M. Pasienski, D. McKay, S. Q. Zhou, D. Ceperley, and B. DeMarco, Phys. Rev. Lett. 102, 055301 (2009).
[Crossref]

Phys. Rev. X (1)

M. A. Norcia, A. W. Young, and A. M. Kaufman, Phys. Rev. X 8, 041054 (2018).
[Crossref]

Other (2)

E. Wolf, Introduction to the Theory of Coherence and Polarization of Light (Cambridge University, 2007).

B. Max and W. Emil, Principles of Optics, 7th expanded ed. (Publishing House of Electronics Industry, 2013).

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Figures (4)

Fig. 1.
Fig. 1. (a) Experimental setup for generating PCRPCAB. (b) The CGH is the computer-generated hologram for the CAB with ${r_0} = 0.8 \;{\rm{mm}}$, $\omega = 80\;{{\unicode{x00B5}{\rm m}}}$, and $a = 0.1$. (c) $2f$ imaging system. BE, beam expender; ${L_1} \sim {L_5}$, thin lens; RGGD, rotating ground-glass disk; CA, circular aperture, which is used as low-pass filter; M, Mirror; LP, linear polarizer; SLM, spatial light modulator; HP, half-wave plate; RPC, radial polarization converter; BPA, beam profile analyzer.
Fig. 2.
Fig. 2. (a) Autofocusing properties of the coherent RPCAB and PCRPCABs. The dashed line denotes the autofocusing position ${z_f} = 40.2\;{\rm{cm}}$. (b)–(d) Intensity patterns of the PCRPCABs (b) as generated and (c) and (d) after passing polarizers.
Fig. 3.
Fig. 3. Intensity patterns in autofocusing plane of the coherent RPCAB and PCRPCABs. (a) Simulation results; (b) experimental results. The unit of each picture is mm.
Fig. 4.
Fig. 4. Simulation results: (a1) and (b1) the distributions (cross line, $y = 0$) of the DOP and the intensity of the PCRPCABs, their completely polarized parts, and unpolarized parts in the autofocusing plane; (a2) and (b2) intensity patterns of the completely polarized part, and the arrows depict their polarization states; (a3) and (b3) intensity patterns of the completely unpolarized part. Experimental results: (c1) and (d1) the distributions of the intensity and DOP in the autofocusing plane, and line graphs are the distributions along $y = 0$. (c2), (c3) and (d2), (d3) the linearly polarized intensity after passing through two orthogonal polarizers.

Equations (9)

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u x ( r , θ ) = C 0 A i ( r 0 r ω 0 ) exp ( a r 0 r ω 0 ) cos ( θ ) ,
u y ( r , θ ) = C 0 A i ( r 0 r ω 0 ) exp ( a r 0 r ω 0 ) sin ( θ ) ,
W ij ( r 1 , θ 1 , r 2 , θ 2 ) = u i ( r 1 , θ 1 ) u j ( r 2 , θ 2 ) μ ( r 1 , θ 1 , r 2 , θ 2 ) .
μ ( r 1 , θ 1 , r 2 , θ 2 ) = exp ( r 1 2 + r 2 2 2 δ 2 ) exp [ r 1 r 2 cos ( θ 1 θ 2 ) δ 2 ] .
W i j ( ρ 1 , ρ 2 , z ) = k 2 4 π 2 z 2 z = 0 d 2 r 1 d 2 r 2 W i j ( 0 ) ( r 1 , r 2 ) × exp [ i k ( ρ 1 r 1 ) 2 z + i k ( ρ 2 r 2 ) 2 z ] ,
W ij ( ρ 1 , φ 1 , ρ 2 , φ 2 , z ) = k 2 4 π 2 z 2 A ~ i P i j exp ( r 1 2 + r 2 2 2 δ 2 ) × exp [ i k 2 z ( r 2 2 + ρ 2 2 r 1 2 ρ 1 2 ) ] r 1 r 2 d r 1 d r 2 ,
A ~ i = C 0 2 A i ( r 0 r 1 ω 0 ) A i ( r 0 r 2 ω 0 ) exp ( a 2 r 0 r 1 r 2 ω 0 ) ,
A l = π 2 J l ( k r 1 ρ 1 z ) e i l ( φ 2 φ 1 ) , B l = J l ( k r 2 ρ 2 z ) , C l = J l + 2 ( k r 2 ρ 2 z ) , D l = J l 2 ( k r 2 ρ 2 z ) , E l = I l + 1 ( r 1 r 2 δ 2 ) , F l = I l 1 ( r 1 r 2 δ 2 ) ,
P xx = l = + A l [ E l ( B l C l e 2 i φ 2 ) + F l ( B l D l e 2 i φ 2 ) ] , P xy = i l = + A l [ E l ( B l + C l e 2 i φ 2 ) F l ( B l + D l e 2 i φ 2 ) ] , P yx = i l = + A l [ E l ( B l C l e 2 i φ 2 ) F l ( B l D l e 2 i φ 2 ) ] , P yy = l = + A l [ E l ( B l + C l e 2 i φ 2 ) ) + F l ( B l + D l e 2 i φ 2 ) ] .

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